If you do the change responsibly you won’t be without email.
I would recommend making a note of your current email addresses.
Create the Google App account, then immediately create the same user accounts.
Go back to dreamhost, and make the change to the domain. You could start to recieve email in your gmail account within a few hours, the time is hard to say, it all depends on how long it takes for the MX record to propagate over the internet.
You won’t lose any mail, the mail will either be delivered to your DH accounts, or eventually to the new Google account. Granted if you delay setting up the new accounts to mirror your old accounts, you could get some bounced email.
Also, to complete the migration, I would recommend, after the google accounts are working, to add a “POP3” account inside gmail for your old DH accounts. This will download all of your old mailbox, into your new google hosted mailbox.
I hope this answers your questions, and I welcome any other google questions you may have.